Distributional Regression

Dingyi Lai / August 2022

Conditional income distribution is critical to understand how income varies in different backgrounds. Such panorama is beneficial for decomposition of income inequality, and can offer a better guide for policy-making accordingly in a further step. In this term paper, theoretical background of generalized additive models for location, scale and shape (GAMLSS) and generalized beta distribution of the second kind (GB2) is introduced, followed by an empirical estimation based on SCF+ data in 2016 in the United States. The parameters are selected via optimization under GAIC criterion. Furthermore, model is evaluated by analysis of quantile residual analysis. Fitted parameters of model are transformed to a grouped histogram across 4 typical ages and 3 races and a 3D income density plot across all ages and races. In conclusion, racial discrepancy widens as age increases, and generally, the probability of earning higher income grows at first and then drops over the age.